Robust optimization approach for pricing and shelf space decisions with uncertain demand

Document Type : Article

Authors

1 Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez avenue, 1591634311, Tehran, Iran

2 Amirkabir University of Technology, Department of Industrial Engineering, 424, Hafez Avenue, Tehran, Iran

Abstract

Pricing and shelf space allocation are two main operational decisions in retailing industry. This study simultaneously optimizes these two decisions in a supply chain with two manufacturers and one retailer under uncertainty of demand and price sensitivity parameters. Two manufacturers have different conditions in terms of parameters affecting demand and production. A robust optimization model and an exact solution approach are developed to find the optimal solution. The results show that price sensitivity, market potential and production costs can have a synergistic effect on optimal values. Moreover, the market potential can be relied on in managerial decisions as it has significantly positive impact on profitability. This parameter is found to be the most important tool for securing profitability of supply chain members.

Keywords


References:
1. Anderson, E.E. and Amato, H.N., A mathematical model for simultaneously determining the optimal brand-collection and display-area allocation", Operations Research, 22(1), pp. 13{21 (1974).
2. Corstjens, M. and Doyle, P. A model for optimizing retail space allocation", Management Science, 27(7), pp. 822{833 (1981).
3. Corstjens, M. and Doyle, P. A dynamic model for strategically allocating retail space", The Journal of 312 M.S. Sajadieh and M. Danaei/Scientia Iranica, Transactions E: Industrial Engineering 29 (2022) 303{319 the Operational Research Society, 34(10), pp. 943{951 (1983).
4. Bultez, A. and Naert, P. Shelf allocation for retailers' pro t", Marketing Science, 7(3), pp. 211{231 (1988).
5. Yang, M.H. An ecient algorithm to allocate shelf space", European Journal of Operational Research, 131(1), pp. 107{118 (2001).
6. Hwang, H., Choi, B., and Lee, M.J. A model for shelf space allocation and inventory control considering location and inventory level e ects on demand", International Journal of Production Economics, 97, pp. 185{195 (2005).
7. Hansen, J.M., Raut, S., and Swami, S. Retail shelf allocation: a comparative analysis of heuristic and metaheuristic
approaches", Journal of Retailing, 86(1), pp. 94{105 (2010).
8. Castelli, M. and Vanneschi, L. Genetic algorithm with variable neighborhood search for the optimal allocation
of goods in shop shelves", Operations Research Letters, 42, pp. 355{360 (2014).
9. Zhou, W. and Piramuthu, S. IoT and supply chain traceability", 1st International Conference on Future Network Systems and Security, FNSS, Paris, June, pp. 11{13 (2015).
10. Amit, R.K., Mehta, P., and Tripathi, R.P. Optimal shelf-space stocking policy using stochastic dominance under supply-driven demand uncertainty", European Journal of Operational Research, 246(1), pp. 339{342 (2015).
11. Hubner, A. and Schaal, K. An integrated assortment and shelf-space optimization model with demand substitution and space-elasticity e ects", European Journal of Operational Research, 261(1), pp. 302{316 (2017).
12. Fatemi Ghomi, S.M.T. and Khalesi, S. A hybrid approach for shelf space planning considering of stochastic demand and display facing area", 13th International Conference on Industrial Engineering (IIEC 2017) (2017).
13. Dusterhoft, T., Hubner, A., and Schaal, K. A practical approach to the shelf-space allocation and replenishment
problem with heterogeneously sized shelves", European Journal of Operational Research, 282(1), pp. 252{266 (2020).
14. Gajjar, H.K. and Adil, G.K. A dynamic programming
heuristic for retail shelf space allocation problem",
Asia-Paci c Journal of Operational Research, 28(2),
pp. 183{199 (2011).
15. Gilland, W.G. and Heese, H.S. Sequence matters:
shelf-space allocation under dynamic customer-driven
substitution", Production and Operations Management,
22(4), pp. 875{887 (2013).
16. Martin-Herran, G. and Taboubi, S. Shelf-space allocation
and advertising decisions in the marketing
channel: a di erential game approach", International
Game Theory Review, 7(3), pp. 313{330 (2005).
17. Hariga, M.A. and Al-Ahmari, A. An integrated retail
space allocation and lot sizing models under vendor
managed inventory and consignment stock arrangements",
Computers & Industrial Engineering, 64(1),
pp. 45{55 (2013).
18. Tsao, Y.C., Lu, J.C., A.n, N., et al. Retailer shelfspace
management with trade allowance: A Stackelberg
game between retailer and manufacturers",
International Journal of Production Economics, 148,
pp. 133{144 (2014).
19. Urban, T.L. An inventory-theoretic approach to product
assortment and shelf-space allocation", Journal of
Retailing, 74(1), pp. 15{35 (1998).
20. Maiti, M.K. and Maiti, M. Multi-item shelf-space
allocation of breakable items via genetic algorithm",
Journal of Applied Mathematics & Computing, 20(1{
2), pp. 327{343 (2006).
21. Hariga, M.A., Al-Ahmari, A., and Mohamed, A.A. A
joint optimisation model for inventory replenishment,
product assortment, shelf space and display area allocation
decisions", European Journal of Operational
Research, 181(1), pp. 239{251 (2007).
22. Ramaseshan, B., Achuthan, N.R., and Collinson, R.
Decision support tool for retail shelf space optimization",
International Journal of Information Technology
& Decision Making, 7(3), pp. 547{565 (2008).
23. Bai, R. and Kendall, G. A model for fresh produce
shelf-space allocation and inventory management with
freshness-condition-dependent demand", Journal of
Computing, 20(1), pp. 78{85 (2008).
24. Gao, J.J. and Yu, L.R. Joint decision model of
variants selection, shelf-space allocation and inventory
control", Xitong Gongcheng Xuebao, 24(5), pp. 614{
620 (2009).
25. Baron, O., Berman, O., and Perry, D. Shelf space
management when demand depends on the inventory
level", Production and Operations Management, 20(5),
pp. 714{726 (2011).
26. Hwang, H., Choi, B., and Lee, G. A genetic algorithm
approach to an integrated 12 problem of shelf space
design and item allocation", Computers & Industrial
Engineering, 56, pp. 809{820 (2009).
27. Ghazavi, E. and Lot , M.M. Formulation of customers'
shopping path in shelf space planning: A
simulation-optimization approach", Expert Systems
with Applications, 55, pp. 243{254 (2016).
28. Flamand, T., Ghoniem, A., Haouari, M., and Maddah,
B. Integrated assortment planning and storewide
shelf space allocation: An optimization-based
approach", Omega, 81, pp. 134{149 (2018).
M.S. Sajadieh and M. Danaei/Scientia Iranica, Transactions E: Industrial Engineering 29 (2022) 303{319 313
29. Schaal, K. and Hubner, A. When does cross-space
elasticity matter in shelf-space planning? A decision
analytics approach", Omega, 80, pp. 135{152 (2018).
30. Sha ee-Gole, S., Nasiri, M., and Taleizadeh, A. Pricing
and production decisions in multi-product single
machine manufacturing system with discrete delivery
and rework", OPSEARCH (2016).
31. Sadjadi, S.J., Asadi, H., Sadeghian, R., et al.
Retailer Stackelberg game in a supply chain with
pricing and service decisions and simple price discount
contract", PLOS ONE, 13(4), e0195109 (2018).
https://doi.org/10.1371/journal.pone.0195109
32. Reyes, P.M. and Frazier, G.V. Goal programming
model for grocery shelf space allocation", European
Journal of Operational Research, 181(2), pp. 634{644
(2007).
33. Murray, C.C., Talukdar, D., and Gosavi, A. Joint
optimization of product price, display orientation and
shelf-space allocation in retail category management,
Journal of Retailing, 86(2), pp. 125{136 (2010).
34. Tan, M. and Wang, H. Retailer's shelf-space and
pricing decisions under revenue sharing contracts",
International Conference on Management and Service
Science (2011).
35. Kurtulus, M. and Toktay, L.B. Category captainship
vs. retailer category management under limited retail
shelf space", Production and Operations Management
Society, 20, pp. 47{56 (2011).
36. Leng, M., Parlar, M., and Zhang, D., Retail Space-
Exchange Problem with Pricing and Space Allocation
Decisions, Production and Operations Management
Society, pp. 1|14 (2011).
37. Li, X. Nukal, S., and Moheb, S. Game theory methodology
for optimizing retailers' pricing and shelf-space
allocation decisions on competing substitutable products",
International Journal of Advanced Design and
Manufacturing Technology, 68, pp. 375{389 (2013).
38. Eisend, M. Shelf space elasticity: A meta-analysis",
Journal of Retailing, 90(2), pp. 168{181 (2014).
39. Wang, S.Y., Sheen, G.J., and Yeh, Y. Pricing
and shelf space decisions with non-symmetric market
demand", International Journal of Production Economics,
169, pp. 233{239 (2015).
40. Hubner, A. and Schaal, K. A shelf-space optimization
model when demand is stochastic and space-elastic",
Omega, 68, pp. 139{154 (2017).
41. Moon, I., Park, K.S, Hao, J., and Kim, D. Joint
decisions on product line selection, purchasing, and
pricing", European Journal of Operational Research,
262(1), pp. 207{216 (2017).
42. Li, H.L. An ecient method for solving linear
goal programming problems", Journal of Optimization
Theory and Applications, 90, pp. 465{469 (1996).
43. Mirzapour, Al-e-hashem, S.M.J., Malekly, H., and
Aryanezhad, M.B. A multi-objective robust optimization
model for multi-product multi-site aggregate production
planning in a supply chain under uncertainty",
International Journal of Production Economics, 134,
pp. 28{42 (2011).
44. Mulvey, J.M., Vanderbei, R.J., and Zenios, S.A. Robust
optimization of large-scale systems", Operations
Research, 43(2), pp. 264{281 (1995).
45. Feng, P. and Rakesh, N. Robust supply chain design
under uncertain demand in agile manufacturing",
Computers & Operations Research, 37(4), pp. 668{683
(2010).
46. Leung, S.C.H., Tsang, S.O.S., Ng., W.L., et al. A
robust optimization model for multi-site production
planning problem in an uncertain environment, European
Journal of Operational Research, 181(1), pp.
224{238 (2007).
47. Wagner, H.M., Principles of Operations Research,
Second Ed., Prentice Hall, New Jersey (1975).
48. Yu, C.S. and Li, H.L. A robust optimization model for
stochastic logistic problem", International Journal of
Production Economics, 64(1{3), pp. 385{397 (2000).
49. Shubik, M. and Levitan, R., Market Structure and Behavior,
Harvard University Press, Cambridge (1980).